Algebra Examples

$\frac{1}{2} + 3 \cdot 2^{2} - 1$

Step 1

Find the common denominator.

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Step 1.1

Write $3 \cdot 2^{2}$ as a fraction with denominator $1$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2}}{1} - 1$

Step 1.2

Multiply $\frac{3 \cdot 2^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2}}{1} \cdot \frac{2}{2} - 1$

Step 1.3

Multiply $\frac{3 \cdot 2^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2} \cdot 2}{2} - 1$

Step 1.4

Write $- 1$ as a fraction with denominator $1$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2} \cdot 2}{2} + \frac{- 1}{1}$

Step 1.5

Multiply $\frac{- 1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2} \cdot 2}{2} + \frac{- 1}{1} \cdot \frac{2}{2}$

Step 1.6

Multiply $\frac{- 1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{3 \cdot 2^{2} \cdot 2}{2} + \frac{- 1 \cdot 2}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{1 + 3 \cdot 2^{2} \cdot 2 - 1 \cdot 2}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2^{2}$ by $2$ by adding the exponents.

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Step 3.1.1

Move $2$ .

$\frac{1 + 3 \cdot (2 \cdot 2^{2}) - 1 \cdot 2}{2}$

Step 3.1.2

Multiply $2$ by $2^{2}$ .

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Step 3.1.2.1

Raise $2$ to the power of $1$ .

$\frac{1 + 3 \cdot (2^{1} \cdot 2^{2}) - 1 \cdot 2}{2}$

Step 3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1 + 3 \cdot 2^{1 + 2} - 1 \cdot 2}{2}$

Step 3.1.3

Add $1$ and $2$ .

$\frac{1 + 3 \cdot 2^{3} - 1 \cdot 2}{2}$

Step 3.2

Raise $2$ to the power of $3$ .

$\frac{1 + 3 \cdot 8 - 1 \cdot 2}{2}$

Step 3.3

Multiply $3$ by $8$ .

$\frac{1 + 24 - 1 \cdot 2}{2}$

Step 3.4

Multiply $- 1$ by $2$ .

$\frac{1 + 24 - 2}{2}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $1$ and $24$ .

$\frac{25 - 2}{2}$

Step 4.2

Subtract $2$ from $25$ .

$\frac{23}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{2}$

Decimal Form:

$11.5$

Mixed Number Form:

$11 \frac{1}{2}$